An Analysis of Analytical Solutions of the Burger-Huxley Equation by (G′/G, 1/G) Expansion Technique

Year 2025, Volume: 3 Issue: 1, 42 - 49, 30.06.2025

Münevver Tuz

https://doi.org/10.63063/jsat.1682099

Abstract

In this study, analytical solutions of Burger-Huxley equation are obtained by using (G′/G, 1/G) expansion method. This method is an efficient technique for solving nonlinear partial differential equations and is applied here to the Burger-Huxley equation, which includes both convection and reaction-diffusion terms, and trigonometric, hyperbolic and rational type solutions of the equation are obtained. Additionally, 2D and 3D graphics were created by giving arbitrary values to the solutions. The obtained solutions help to better understand the physical and mathematical structure of the equation and serve as a guide for solving similar type of differential equations.

Keywords

(G′/G, 1/G) expansion method, nonlinear partial differential equation, balancing term, analytical solution.

Burger-Huxley Denkleminin Analitik Çözümlerinin (G′/G, 1/G) Genişleme Tekniği ile Analizi

Abstract

Bu çalışmada, Burger-Huxley denkleminin analitik çözümleri (G′/G, 1/G) genişleme yöntemi kullanılarak elde edilmiştir. Bu yöntem, doğrusal olmayan kısmi diferansiyel denklemleri çözmek için etkili bir tekniktir ve burada hem konveksiyon hem de reaksiyon-difüzyon terimlerini içeren Burger-Huxley denklemine uygulanmıştır, deklemin trigonometrik, hiperbolik ve rasyonel tip çözümleri elde edilmiştir. Ayrıca, çözümlere keyfi değerler verilerek 2 ve 3 boyutlu grafikler oluşturulmuştur. Elde edilen çözümler, denklemin fiziksel ve matematiksel yapısını daha iyi anlamaya yardımcı olur ve benzer tipteki diferansiyel denklemleri çözmek için bir rehber görevi görür.

Keywords

(G′/G, 1/G) genişleme yöntemi, doğrusal olmayan kısmi diferansiyel denklem, dengeleme terimi, analitik çözüm.

Ethical Statement

Ethical approval is not required.

Supporting Institution

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Thanks

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